Use the image to answer the question.

Question

An illustration shows the first quadrant of a coordinate plane titled Population of a City Since 1900.
The x-axis shows years since 1900 and ranges from 0 to 80 in increments of 10. The y-axis shows population per thousand and ranges from 0 to 80 in increments of 5. Nine points are plotted on the graph. The points are plotted at approximate coordinates left parenthesis 0 comma 20 right parenthesis, left parenthesis 10 comma 28 right parenthesis, left parenthesis 20 comma 30 right parenthesis, left parenthesis 30 comma 35 right parenthesis, left parenthesis 40 comma 47 right parenthesis, left parenthesis 50 comma 55 right parenthesis, left parenthesis 60 comma 57 right parenthesis, left parenthesis 70 comma 68 right parenthesis, and left parenthesis 80 comma 66 right parenthesis. An upward slanting line starts at left parenthesis 0 comma 20 right parenthesis and continues to left parenthesis 60 comma 57 right parenthesis.

The population growth of a city since 1900 is represented by a linear model. Interpret the slope and the y
-intercept.

(1 point)
Responses

For every year since 1900, the population grew by approximately 650. In 1900, the population was 20,000.
For every year since 1900, the population grew by approximately 650. In 1900, the population was 20,000.

For every year since 1900, the population grew by approximately 300. In 1900, the population was 0.
For every year since 1900, the population grew by approximately 300. In 1900, the population was 0.

For every year since 1900, the population grew by approximately 1,590. in 1900, the population was 20,000.
For every year since 1900, the population grew by approximately 1,590. in 1900, the population was 20,000.

For every 0.65 of a year since 1900, the population grew by approximately 1,000. In 1900, the population was 20,000.
For every 0.65 of a year since 1900, the population grew by approximately 1,000. In 1900, the population was 20,000.

Answer 1

To find the slope and the y-intercept from the information given, we can interpret the coordinates and the characteristics of the line plotted in the illustration.

1. Y-Intercept: The point (0, 20) on the graph indicates that in the year 1900 (which corresponds to x = 0), the population per thousand was approximately 20. Thus, the population at that time would be 20,000 people (since the y-axis is in thousands).

2. Slope: The slope can be calculated using two points on the line. For instance, we can use the points (0, 20) and (70, 68).

   • The change in population from year 0 to year 70 is from 20 to 68 (a change of 48).
   • The change in time is from year 0 to year 70 (a change of 70 years).
   • Therefore, the slope (m) is calculated as: \[ \text{slope} = \frac{\text{change in population}}{\text{change in time}} = \frac{68 - 20}{70 - 0} = \frac{48}{70} \approx 0.686 \]
   • This means that the population grows by approximately 0.686 thousand people per year, which can be rounded to approximately 650 people per year when considering population in full numbers.

Given these interpretations, we can conclude:

• The population grew by around 650 people each year since 1900.
• The initial population in 1900 was 20,000 people.

Thus, the correct response from the choices provided is: For every year since 1900, the population grew by approximately 650. In 1900, the population was 20,000.